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SilverSight/data/spectral_codebook.json
allaun 4ea68bcecc feat(spectral): gap-aware spectral codebook generator with exact char-poly fingerprints 
Implements the Next Steps of docs/SPECTRAL_CODEBOOK_ANALYSIS.md as
python/spectral_codebook.py (stdlib-only; NumPy optional fast path):

- Parses the 250 8x8 braid adjacency matrices from PIST/Matrices250.lean.
- Primary fingerprint: exact integer characteristic-polynomial
  coefficients via Faddeev-LeVerrier in Fraction arithmetic (196 unique
  over 238 distinct matrices, vs 179 unique lambda at 4dp; 6 cospectral
  non-identical groups; 11 exact-duplicate matrix groups / 23 ids).
- Corrects the analysis doc: the 9 'mid band' lambda in (0.5,1) are
  power-iteration non-convergence artifacts - exact rho = 1.0 for all 9
  (peripheral spectra). spectral_radius is now the exact max root
  modulus (numpy eigvals or Durand-Kerner on the exact char poly);
  power-iteration lambda kept only for traceability.
- Gap-aware quantization: dedupe to 238 distinct matrices, boundaries at
  gaps > 3x median gap, min-support guard (>=10 distinct per cluster),
  sparse-tail outlier flagging above lambda ~= 7.66. Result: 9 clusters.
- Round trip encode(matrix) -> (codeword, index) -> decode -> equation_id
  verified bijective over all 250 in tests/test_spectral_codebook.py.
- 278-row RRC/Q16_16Manifold corpus: 28 extra rows are repeated ids;
  boundaries reproduce exactly, no new gaps or clusters.
- Emits data/spectral_codebook.json (schema spectral_codebook_v2) with
  explicit collision classes; docs/SPECTRAL_CODEBOOK_GENERATOR.md notes
  the hashMatrix base-5 injectivity gap and the ClassifyN threshold
  (1.5/4.0 Q16.16) vs analysis-doc (0.5/1.0) mismatch.

Co-Authored-By: Claude Fable 5 <noreply@anthropic.com>
2026-07-01 20:39:40 -05:00

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{
"schema": "spectral_codebook_v2",
"generated": "2026-07-01",
"source": "formal/SilverSight/PIST/Matrices250.lean",
"matrix_count": 250,
"lambda_semantics": "spectral_radius is the exact max root modulus of the integer characteristic polynomial (charpoly); lambda_power_iteration is the legacy estimate and is unreliable on peripheral spectra",
"quantization": {
"method": "gap_aware_deduped_min_support",
"gap_factor": 3.0,
"min_support": 10,
"median_gap": 0.021671,
"threshold": 0.065013,
"boundaries": [
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],
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],
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],
"sparse_tail_cutoff": 7.656836
},
"clusters": [
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"count": 35,
"distinct_matrices": 31,
"lambda_min": 0.0,
"lambda_max": 0.0,
"sparse_tail_members": 0
},
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"codeword": "C1",
"count": 20,
"distinct_matrices": 20,
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},
{
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},
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},
{
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},
{
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},
{
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},
{
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},
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